The present invention relates to modulation systems for transmission of digital data over a channel.
Some existing digital transmission systems incorporate precoding and shaping. Shaping is a method of selecting a signal point sequence from a subset of all allowable signal point sequences. The selection is based on the respective powers of the candidate sequences. The objective of shaping is to achieve a non-uniform, Gaussian-like distribution over an expanded constellation, so as to reduce the average signal power at the same data rate. This power reduction is called shaping gain. Trellis shaping is one of the well-known shaping techniques. In this technique, the transmitter selects a sequence by a search through the trellis diagram of a convolutional shaping code, and the set of all candidate sequences is not a simple Cartesian product of finite-dimensional regions. Trellis shaping uses an expanded signal constellation in which the symbols have a plurality of representations.
Another practicable (nonlinear) processing in digital transmission systems operating over InterSymbol Interference (ISI) channels is precoding. The precoder eliminates the need for a Decision Feedback Equalizer (DFE) at the receiver, which provides two prominent advantages. Firstly, it enables the use of coding over ISI channels in the same manner as for channels without ISI. The operation of the DFE requires zero delay decisions whereas any coding scheme entails some delay in the decision path. Thus channel coding cannot be combined with DFE in a direct way. Secondly, error propagation is ascribed to the DFE but avoided in the alternative scheme that utilizes a precoder. In this scheme, the channel response has to be known at the transmitter. There are numerous ways to combine precoding with shaping. One of these combinations is known as trellis precoding which combines trellis shaping and precoding.
It is well-known that the sequence at the output of the precoder is uncorrelated regardless of the channel response. However, when shaping is combined with preceding, then the constrained sequences may no longer be uncorrelated. A digital transmitter is usually limited to meet a required spectral mask. Consequently, the transmit spectrum may not meet the mask when the sequence at the output of the precoder is not uncorrelated, and hence no longer has a white spectrum. Furthermore, the correlation between the transmitted samples may be channel dependent.
Trellis shaping for modulation systems is described in U.S. Pat. No. 5,150,381 to Forney, Jr. et al.; in Forney xe2x80x9cTrellis Shapingxe2x80x9d IEEE Trans. Inform. Theory, vol. 38, no. 2, pp. 281-300, March 1992; and in Eyubo{haeck over (g)}lu et al. xe2x80x9cTrellis precoding: combined coding, precoding and shaping for intersymbol interference channels,xe2x80x9d IEEE Trans. Inform. Theory, vol. 38, no. 2, pp. 301-314, March 1992.
Another shaping method is described in Fischer et al. xe2x80x9cDynamics limited precoding, shaping, and blind equalization for fast digital transmission over twisted pair lines,xe2x80x9d IEEE J. Select. Areas on Commun., vol. 13, no. 9, pp. 1622-1633, December 1995.
Viterbi search methods are described in:
A. J. Viterbi, xe2x80x9cError bounds for convolutional codes and an asymptotically optimum decoding algorithm.xe2x80x9d IEEE Trans. Inform. Theory vol.IT-13, pp.260-9, April 1967; and
D. G. Forney, Jr., xe2x80x9cThe Viterbi Algorithm.xe2x80x9d Proc. IEEE vol.61, pp.268-78, March 1973.
The disclosures of all publications mentioned in the specification and of the publications cited therein are hereby incorporated by reference.
The present invention seeks to provide a method applicable to transmitters that incorporate shaping and precoding. The method maps a data sequence to an uncorrelated signal point sequence. The method involves a modification of the coefficients of the feedback filter of the precoder and an addition of a whitening filter at the output of the precoder that compensates for the above modification. The receiver suitable to reconstruct the source data of this transmitter over the channel is the receiver used for the original transmitter without the modification and the additional filter.
There is thus provided in accordance with a preferred embodiment of the present invention a method for substantially reducing correlation between samples within a post-whitening signal point sequence generated by a transmitter employing a shaping procedure and including a precoding unit having a feedback filter operative to generate a set of candidate signal point sequences {x0(z), x1(z), . . . ,xSxe2x88x921(z)} and an output, the transmitter being operative to transmit input data over a channel toward a receiver, the channel being characterized by a monic equivalent channel response h(z), the method including using the shaping method and the precoding unit to generate the set of candidate signal point sequences xj(z), and selecting a pre-whitening signal point sequence from the set of candidate signal point sequences, for each sample of input data, wherein generation of each component of each individual candidate sequence is partly based on processing past components of the individual candidate sequence, including modifying the feedback filter of the precoding unit so that its response is h(z)w(z)xe2x88x921 rather than h(z)xe2x88x921, and adding a whitening filter with response w(z) at the output of the precoding unit, wherein the whitening filter compensates for the modifying step such that a receiver constructed and operative to receive data from a transmitter whose precoder""s feedback filter has coefficients representing the monic equivalent channel response h(z), via the channel, is also able to receive data from a transmitter which performs the modifying and adding steps, via the channel.
Further in accordance with a preferred embodiment of the present invention the step of selecting an interim signal point sequence is at least partly determined by the relative powers of various candidate sequences in the set of candidate sequences.
Still further in accordance with a preferred embodiment of the present invention the set of candidate point sequences is associated with a finite state trellis diagram and the selecting step includes a search through the trellis diagram.
Additionally in accordance with a preferred embodiment of the present invention the selecting step includes a Viterbi-algorithm type search.
Also in accordance with a preferred embodiment of the present invention the selecting step is also operative to reduce the peak power required to transmit the post-whitening signal point sequence.
Further in accordance with a preferred embodiment of the present invention the pre-whitening signal point sequence is selected by the shaping algorithm, for each sample of input data, such that the input data is recoverable at the receiving end of the channel.
Still further in accordance with a preferred embodiment of the present invention at least the step of modifying coefficients of the feedback filter of the precoding unit is determined in a preliminary adaptation stage in which the transmitter starts operating in a state wherein the response of the feedback filter of its preceding unit is h(z)xe2x88x921.
Additionally in accordance with a preferred embodiment of the present invention the adaptation stage includes a least mean squares adaptation.
Further in accordance with a preferred embodiment of the present invention the whitening filter includes a Finite Impulse Response (FIR) filter.
Still further in accordance with a preferred embodiment of the present invention the whitening filter includes an Infinite Impulse Response (IIR) filter.
Additionally in accordance with a preferred embodiment of the present invention the preceding unit includes an array of parallel precoders.
Further in accordance with a preferred embodiment of the present invention the step of selecting a pre-whitening signal point sequence is operative to reduce the peak power of the pre-whitening signal point sequence.
There is also provided in accordance with another preferred embodiment of the present invention apparatus for substantially reducing correlation between samples within a post-whitening signal point sequence, the apparatus including a transmitter operative to transmit input data over a channel toward a receiver, the channel being characterized by a monic equivalent channel response h(z), the transmitter including a shaping unit operative to select a pre-whitening signal point sequence from a set of candidate signal point sequences, for each sample of input data, and a precoding unit operative to generate the set of candidate signal point sequences xj(z) wherein generation of each component of each individual candidate sequence is partly based on processing past components of the individual candidate sequence, the precoding unit including a feedback filter, whose coefficients represent the response h(z)w(z)xe2x88x921, an output, and a whitening filter with response w(z) at the output of the precoding unit, wherein the whitening filter is operative to compensate for the w(z) factor in the feedback filter, and a receiver, constructed and operative to receive data from the transmitter whose precoder""s feedback filter has coefficients representing the response h(z)xe2x88x921, via the channel, is also operative to receive data from a transmitter which includes the preceding units, via the channel.
Further in accordance with a preferred embodiment of the present invention the response w(z) of the whitening filter is set such that the samples at the output of the whitening filter are practically uncorellated.